To begin with my argument, I’ll tell a story of my own. In the summer vacation, with generative AI I developed a online notebook application whose design may be innovative and unique in my view. To complete this work I, a high school student, used AI to generative tons of code. People’s creativity comes from their whims, and most of them just evaporate for their limited capbility. However, when AI’s knowledge and skills shelter the whims from the complexity of the reality, our whims could transform into a true, creativity, rather than fade out in our mind. This is the first point.
Secondly, AI proivdes a more accessible platform for every one to gain knowledge. We can’t deny that creativity is based on knowledge. Primitive human can’t imagine the Internet while the under-educated people can’t understand generative AI’s structure as well. Today ,those difficult conception could be explained by AI, those hidden tips could be unearthed from the corner of the Internet by AI, and those people, who consist the most part of the world and can’t accept the best education, could have the most patient teacher. So AI will definitely enhance creativity by expanding the soil it comes from.
Lastly, if we omit the content I had explained and stubbornly insist AI hinder the creativity, saying like “AI’s convenient answer prevent people from thinking” or some prediction about a dark future with AI, I will say that it’s not AI hinder our creativity. When employers replace workers with ai without considering their lives, when some people depending on ai give up thinking deeply, the faughts were always on people ourselves. It may be inappropriate structure of society or the laziness of human nature. AI is just a knife and people decide who it will attack.
As a summry, AI has enhanced and will constantly enhance human’s creativity by realizing the whims that we could already quit and popularizing the knowledge be the basical root of creativity.
Class 2
Something about Chinese Culture
Unity of Human and Nature
Heaven has its seasons,erath has its engery,material has its quality, and craftmans have their skills.
drain the pounds to catch the fish
Creative Spirit of Craftsmanship
We polish the lacquer and the lacquer also polishes us.
People-oriented thinking
Filial Piety(孝顺)
the benevolent love the people.
treat the elders of others as your own, treat the kids of others as your own
harmony without uniformity
all things carreid Yin and embrace Yang,through the collection(?) of Qi to achieve harmony
If three corners of a parallelogram are , , and , what are all three of the possible fourth corners? Draw those three parallelograms.
a triangle with another three outer vertices
T13
Review Question. In xyz space, where is the plane of all linear combinations of and ?
equal to the linear combination of i and j().
so it’s the plane xOy
T17
What combination produces ? Express this question as two equations for the coefficients c and d in the linear combination.
T19
Restricted only by and draw the “cone” of all combinations .
a angle that has the origin as the vertex(we should paint all the points between u and v black)
T23
If you look at all combinations of those , is there any vector that can’t be produced from ? Different answer if are all in ______.
(1):no.
(2):a plane
Challange Problems
T24
How many corners does a cube of side 2 have in 4 dimensions? What is its volume? How many 3D faces? How many edges? Find one edge.
(1):every component of every vertex’s coordinate has two value, so there are vertices.
(2):volume:
(3):every 3d faces means a restriction of one component, so
(4):every edge means a restriction of three components, and the last component’s two value represents two vertex it connects. so
T25
Find two different combinations of the three vectors and and that produce . Slightly delicate question: If I take any three vectors in the plane, will there always be two different combinations that produce ?
(1)
.
so for each
is a solution
(2)
No. eg:
Yes when there are two vectors in that are linearly dependent.
T26
The linear combinations of and fill the plane unless ________. Find four vectors with four nonzero components each so that their combinations produce all vectors in four-dimensional space.
(1)
(2)
(do some elementary row operation on Identity Matrix)
T27
Write down three equations for so that . Write this also as a matrix equation . Can you somehow find for this ?
In n-D space we can found at most vector such that:
An example in 3-D space(the one on the book)
The construction is Obviously()
Chosen a vector, the others must be in a semisphere. We say two semisphere is seperated by plane A.
And we notice that: if two vector’s shadow on plane A construct a acute angle, their dot product must be positive, transformed it into a 2-D problems which is easy to solve.
Generalize to n-D
We choose a vector , and it can be written as (with some rotation)
so
then transformed it into the (n-1)-D situation.
The construction can be easily give during the induction
Another Proof
given by Bing!
Lemma: Radon Partition
In n-D space, point could be divided to two convex hull with intersection.
vector must be dependent: (the second condition can be satisfied by add another all-1 dimension).
so divide the vector by sign of we got:,so divide the eqution by , you get one point() in the intersection.